What is the easiest way for my husband to adopt my daughter who's biological father is not in the picture and has never been named in any paperwork?

The ONLY way is to go to a local Family Court and file a petition for adoption. You are best off getting an attorney to advise you and prepare the proper paperwork.

If the chids father is not on the birth certificate, there has never been any proof of paternity, no custody order, no child support order,

Actually at this point it is going to be a lot harder than if there was proof.

But you will have to first prove he is the father, and then have him sign over his rights to allow adoption.